Results 1 to 10 of about 35,012 (233)
Lift and Relax for PDE-Constrained Inverse Problems in Seismic Imaging [PDF]
IEEE Transactions on Geoscience and Remote Sensing, 2021 We present Lift and Relax for Waveform Inversion (LRWI), an approach that mitigates the local minima issue in seismic full waveform inversion (FWI) via a combination of two convexification techniques. The first technique (Lift) extends the set of variables in the optimization problem to products of those variables, arranged as a moment matrix.
Zhilong Fang, Laurent Demanet
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Advanced numerical methods for inverse problems in evolutionary PDEs
, 2017 Michal Galba
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Probabilistic numerical methods for PDE-constrained Bayesian inverse problems [PDF]
AIP Conference Proceedings, 2017 This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for the impact of the discretisation of the forward problem.
Cockayne, J +3 more
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On some nonlinear fractional PDEs in physics
Bibechana, 2014 In this paper, we applied relatively new fractional complex transform (FCT) to convert the given fractional partial differential equations (FPDEs) into corresponding partial differential equations (PDEs) and Variational Iteration Method (VIM) is to find
Jamshad Ahmad, Syed Tauseef Mohyud-Din
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The Cauchy problem for the Pavlov equation [PDF]
, 2014 Commutation of multidimensional vector fields leads to integrable nonlinear dispersionless PDEs arising in various problems of mathematical physics and intensively studied in the recent literature.
Grinevich, P. G., Santini, P. M., Wu, D.
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Model Reduction and Neural Networks for Parametric PDEs [PDF]
, 2020 We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning, in combination with ideas from model ...
Bhattacharya, Kaushik +3 more
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Inverse problems for PDEs: Models, computations and applications [PDF]
SCIENTIA SINICA Mathematica, 2018 Inverse problems for partial differential equations (PDEs) are of great importance in the areas of applied mathematics, whichcover different mathematical branches including PDEs, functional analysis, nonlinear analysis,optimizations, regularization and numerical analysis.
Cheng Jin, Liu Jijun, Zhang Bo
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Continuous analogue to iterative optimization for PDE-constrained inverse problems [PDF]
Inverse Problems in Science and Engineering, 2018 The parameters of many physical processes are unknown and have to be inferred from experimental data. The corresponding parameter estimation problem is often solved using iterative methods such as steepest descent methods combined with trust regions. For a few problem classes also continuous analogues of iterative methods are available.
Boiger, R. +3 more
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Machine Learning: Science and Technology, 2023 We present novel approximates of variational losses, being applicable for the training of physics-informed neural networks (PINNs). The formulations reflect classic Sobolev space theory for partial differential equations (PDEs) and their weak ...
Juan-Esteban Suarez Cardona +1 more
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Mathematics, 2023 Physics-Informed Neural Networks (PINNs) improve the efficiency of data utilization by combining physical principles with neural network algorithms and thus ensure that their predictions are consistent and stable with the physical laws.
Zhixiang Liu +4 more
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